Scrutiny of principle of energy survival in beam-columns and analytical solution of governing partial nonlinear differential equation by new approach AYM

In this manuscript, we investigate and solve a complicated highly nonlinear differential equations in the beam-column in the Energy Survival Principal equation on the beam-column to show the ability of the first invented method which we named it AYM (Akbari Yasna’s Method). Certainly, we know that nonlinear beam-column process are very complex, and the governing differential equations governing them are nonlinearity complex. In this paper we present a new analytical solution which can easily analyze all such problems and make a great evolution in the nonlinear designing in the solid engineering (civil and mechanical and etc.). Finally, this scientific approach can create a great phenomenon in the analytical solution of nonlinear problems in engineering sciences, especially in the solids engineering.